Question

Fan + Medal
Calculus help / checking

Answer 1

Would this be correct?

Answer 2

Look at the limit as it comes from the left and right

Answer 3

Or I am thinking it is Does not exist since it says the limit -> 3 not 3+ or 3-

Answer 4

Good!

Answer 5

A little confused. I think it y=2 Since you take the leading coefficients 2x^3/x^4 which gets you 2/x

Answer 6

when \(x\) approaches to \(+\infty\) or to \(-\infty\), then I can rewrite your function as below:
\[\huge f\left( x \right) = \frac{{\frac{2}{x} + \frac{9}{{{x^4}}}}}{{1 + \frac{{81}}{{{x^4}}}}}\]

Answer 7

What are the asymptotes of the function?

Answer 8

Hey Michele haha :P

Answer 9

oops..
\[\huge f\left( x \right) = \frac{{\frac{2}{x} + \frac{9}{{{x^4}}}}}{{1 - \frac{{81}}{{{x^4}}}}}\]

Answer 10

lol :) @Astrophysics the same idea!!

Answer 11

x=3 x=-3 y=0

Answer 12

I think that the end behaviour, means the behaviour at the boundary of the real line
what do you think @Astrophysics ?

Answer 13

Yeah pretty much, you look at where x is getting really big/ small in simple terms

Answer 14

So check where x -> + inf and x-> - inf

Answer 15

The question says most closely matches. So it would be y=0 or would it be y=2

Answer 16

hint:
when \(x\) approaches to \(+\infty\) or to \(-\infty\), we have this:
\[\Large \frac{2}{x} \to 0,\quad \frac{9}{{{x^4}}} \to 0,\quad \frac{{81}}{{{x^4}}} \to 0\]

Answer 17

So y=0 is the correct answer

Answer 18

that's right!

Answer 19

:)

Answer 20

what about...